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2000005307

Level:

Use the graphs of the functions

f (x) = x + 3

and

g (x) = x - 1

to find the solution set of the following inequality.

\frac{x + 3}{x - 1} \leq 0

x \in [- 3; 1)

x \in [- 3; 1]

x \in (1; + \infty)

x \in (- 1; + \infty)

2000005306

Level:

Use the graphs of the functions

f (x) = x^{2} - 4

and

g (x) = x + 2

to find the solution set of the following inequality.

\frac{x^{2} - 4}{x + 2} \geq 0

x \in [2; + \infty)

x \in (2; + \infty)

x \in (- \infty; - 2) \cup (2; + \infty)

x \in (- \infty; - 2] \cup [2; + \infty)

2000005303

Level:

Use the graphs of the functions

f (x) = x^{2} - 5 x + 4

and

g (x) = x^{2} + 2 x - 3

to find the solution set of the following equation.

\frac{x^{2} - 5 x + 4}{x^{2} + 2 x - 3} = 1

\emptyset

{1}

{- 3; 4}

{- 3; 1; 4}

2000005302

Level:

Use the graphs of the functions

f (x) = x^{2} - x - 6

and

g (x) = x - 3

to find the solution set of the following equation.

\frac{x^{2} - x - 6}{x - 3} = 1

{- 1}

{3}

{- 1; 3}

{- 2; 3}

2000005202

Level:

From the given functions select a function

f

so that its inverse function

f^{- 1}

has the graph shown in the picture.

f (x) = \sqrt{x + 1}; x \in [- 1; \infty)

f (x) = x^{2} - 1; x \in (- \infty; 0]

f (x) = \frac{1}{\sqrt{x - 1}}; x \in [- 1; \infty)

f (x) = x^{2} - 1; x \in R

2000005201

Level:

Which of the following functions is the inverse function to the function

f (x) = - 3 x + 2

f^{- 1} (x) = - \frac{x}{3} + \frac{2}{3}

f^{- 1} (x) = \frac{x}{3} - \frac{2}{3}

f^{- 1} (x) = 2 x - 3

f^{- 1} (x) = - \frac{x}{3} + 1

2000004405

Level:

We randomly choose natural numbers from between

1

20

so that each choice is equally probable. Let the event

A

be: the chosen number is divisible by

5

. Let the event

B

be: the chosen number is smaller than

11

. Find

P (A ∣ B)

\frac{1}{5}

\frac{2}{11}

\frac{1}{4}

\frac{2}{5}

2000004311

Level:

The function

f

is graphed in the picture. Which of the following is its equation?

f (x) = | x^{2} - 1 | - 1

f (x) = | x^{2} + 1 | - 1

f (x) = | x^{2} + 1 | + 1

f (x) = | x^{2} - 1 | + 1

2000004310

Level:

The function

f

is graphed in the picture. Which of the following is its equation?

f (x) = x^{2} - 4 | x |

f (x) = | x^{2} - 4 x |

f (x) = | x^{2} | - 4 x

f (x) = | x^{2} | + 4 x

2000004309

Level:

The function

f

is graphed in the picture. Which of the following is its equation?

f (x) = - | x^{2} - 4 |

f (x) = - | x^{2} + 4 |

f (x) = - | x^{2} | - 4

f (x) = - | x^{2} | + 4

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